Logic of imagination. Echoes of Cartesian epistemology in contemporary philosophy of mathematics and beyond

Descartes’ Rules for the direction of the mind presents us with a theory of knowledge in which imagination, considered as an “aid” for the intellect, plays a key role. This function of schematization, which strongly resembles key features of Proclus’ philosophy of mathematics, is in full accordance with Descartes’ mathematical practice in later works such as La Géométrie from 1637. Although due to its reliance on a form of geometric intuition, it may sound obsolete, I would like to show that this has strong echoes in contemporary philosophy of mathematics, in particular in the trend of the so called “philosophy of mathematical practice”. Indeed Ken Manders’ study on the Euclidean practice, along with Reviel Netz’s historical studies on ancient Greek Geometry, indicate that mathematical imagination can play a central role in mathematical knowledge as bearing specific forms of inference. Moreover, this role can be formalized into sound logical systems. One question of general epistemology is thus to understand this mysterious role of the imagination in reasoning and to assess its relevance for other mathematical practices. Drawing from Edwin Hutchins’ study of “material anchors” in human reasoning, I would like to show that Descartes’ epistemology of mathematics may prove to be a helpful resource in the analysis of mathematical knowledge.     

Phenomenal consciousness with infallible self-representation

In this paper, I argue against the claim recently defended by Josh Weisberg that a certain version of the self-representational approach to phenomenal consciousness cannot avoid a set of problems that have plagued higher-order approaches. These problems arise specifically for theories that allow for higher-order misrepresentation or—in the domain of self-representational theories—self-misrepresentation. In response to Weisberg, I articulate a self-representational theory of phenomenal consciousness according to which it is contingently impossible for self-representations tokened in the context of a conscious mental state to misrepresent their objects. This contingent infallibility allows the theory to both acknowledge the (logical) possibility of self-misrepresentation and avoid the problems of self-misrepresentation. Expanding further on Weisberg’s work, I consider and reveal the shortcomings of three other self-representational models—put forward by Kreigel, Van Gulick, and Gennaro—in order to show that each indicates the need for this sort of infallibility. I then argue that contingent infallibility is in principle acceptable on naturalistic grounds only if we attribute (1) a neo-Fregean kind of directly referring, indexical content to self-representational mental states and (2) a certain ontological structure to the complex conscious mental states of which these indexical self-representations are a part. In these sections I draw on ideas from the work of Perry and Kaplan to articulate the context-dependent semantic structure of inner-representational states.     

Alpha factor analysis of infallible variables

The relationship between the factor pattern,F, derived from fallible (containing measurement error) observations on variables and the factor pattern,F*, derived from infallible observations on variables is investigated. A widely believed relationship betweenF andF*, viz.,F*=AF whereA is a diagonal matrix containing the inverses of the square roots of the reliabilities of the variables, is shown to be false for several factor analytic techniques. Under suitable assumptions, it is shown that for Kaiser and Caffrey's alpha factor analysisF* andF are related byF*=AF. Empirical examples for which the corresponding elements ofF* andAF are equal to two decimal places are presented. The implications of the equality ofF* andAF for alpha factor analysis are discussed.I wish to acknowledge the generous assistance of Drs. Chester W. Harris and Henry F. Kaiser in the execution of the research reported in this paper.     

Skepticism and justification

Synthese - This paper discusses the skeptical argument presented by Keith Lehrer in his paper ‘Why Not Scepticism?’. It is argued that Lehrer's argument depends on unacceptable...     

Teleological epistemology

Philosophical Studies - It is typically thought that some epistemic states are valuable—knowing, truly or accurately believing, understanding (to name a few). These are states it’s...     

Decision-theoretic epistemology

In this paper, I examine the possibility of accounting for the rationality of belief-formation by utilising decision-theoretic considerations. I consider the utilities to be used by such an approach, propose to employ verisimilitude as a measure of cognitive utility, and suggest a natural way of generalising any measure of verisimilitude defined on propositions to partial belief-systems, a generalisation which may enable us to incorporate Popper's insightful notion of verisimilitude within a Bayesian framework. I examine a dilemma generated by the decision-theoretic procedure and consider an adequacy condition (immodesty) designed to ameliorate one of its horns. Finally, I argue in a sceptical vein that no adequate verisimilitude measure can be used decision-theoretically.I am grateful to Philip Percival for his very useful comments and criticism on earlier drafts. This paper was written with the support of a Scheuer fellowship, for which I am most thankful.     

Utilitarian epistemology

Standard epistemology takes it for granted that there is a special kind of value: epistemic value. This claim does not seem to sit well with act utilitarianism, however, since it holds that only welfare is of real value. I first develop a particularly utilitarian sense of “epistemic value”, according to which it is closely analogous to the nature of financial value. I then demonstrate the promise this approach has for two current puzzles in the intersection of epistemology and value theory: first, the problem of why knowledge is better than mere true belief, and second, the relation between epistemic justification and responsibility.     

Melancholic epistemology

Too little attention has been paid by philosophers to the cognitive and epistemic dimensions of emotional disturbances such as depression, grief, and anxiety and to the possibility of justification or warrant for such conditions. The chief aim of the present paper is to help to remedy that deficiency with respect to depression. Taxonomy of depression reveals two distinct forms: depression (1) with intentionality and (2) without intentionality. Depression with intentionality can be justified or unjustified, warranted or unwarranted. I argue that the effort of Aaron Beck to show that depressive reasoning is necessarily illogical and distorted is flawed. I identify an essential characteristic of that depression which is a mental illness. Finally, I describe the potential of depression to provide credal contact with important truths.Many persons helped in writing this paper. Special thanks are owed to my wife, Patricia Sedgeman Graham, as well as to Richard Garrett and Hugh LaFollette.     

Turtle epistemology

In “Justification Without Awareness”, Michael Bergmann divides internalist epistemologies into those with a strong awareness requirement and those with a weak awareness requirement; he presents a dilemma, hoisting the “strongs” on one horn, and the “weaks” on the other. Here I reply on behalf of the strong-awareness view, presenting what I take to be a more satisfactory, and more fundamental, reply to Bergmann than I believe has been offered by his other critics, and in particular by Rogers and Matheson in their “Bergmann’s dilemma: exit strategies for internalists,” with which I am in partial agreement.     

Market epistemology

Synthese - According to Margaret Gilbert’s collective epistemology, we should take attributions of beliefs to groups seriously, rather than metaphorically or as reducible to individual...     

Interdisciplinary epistemology

In commemorating Piaget we should not remember his psychology alone. He hoped for a biologically grounded epistemology, which would require interdisciplinary effort. This paper mentions some recent research in biology, embryology, and philosophy that is consonant with Piaget's epistemological aims. The authors do not cite Piaget as a prime intellectual influence, there being no distinctive Piagetian methodology outside psychology. But they each mention him as someone whose work is relevant to theirs and whose interdisciplinary aims will be achieved only if studies like these can be integrated in the future.This paper originally appeared as a chapter in the 1983 book Jean Piaget: An Interdisciplinary Critique, edited by Sohan Modgil, Celia Modgil, and Geoffrey Brown, and published by Routledge & Kegan, Paul, London.     

Anti-luck epistemology

In this paper, I do three things. First, I offer an overview of an anti-luck epistemology, as set out in my book, Epistemic Luck (Oxford University Press, Oxford 2005). Second, I attempt to meet some of the main criticisms that one might level against the key theses that I propose in this work. And finally, third, I sketch some of the ways in which the strategy of anti-luck epistemology can be developed in new directions.